The radius of gyration of a uniform disc about a line perpendicular to the disc equals ilts radius. Find the distance of the line from the centre.

Explanation

To solve the problem, we need to find the distance \( d \) from the center of a uniform disc to a line perpendicular to the disc such that the radius of gyration about that line equals the radius of the disc \( r \).

### Step-by-Step Solution:

1. **Understanding the Moment of Inertia of the Disc**:
The moment of inertia \( I \) of a uniform disc about an axis through its center and perpendicular to its plane is given by:
\[
I = \frac{1}{2} M r^2
...